Question

# A firecracker exploding on the surface of a lake is heard as two sounds a time interval t apart by a man on a boat close to the water surface. Sound travels by a speed v in the air. The distance from the exploding firecracker to the boat is:

A
uvtu+v
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B
t(u+v)uv
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C
t(uv)uv
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D
uvtuv
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Solution

## The correct option is D uvtu−vSound reaches the man via two media (water and air). Time taken by sound wave in air medium is tair=xvair=xvx is the distance between the source and observer. Time taken by sound wave in water medium is tw=xvw=xuHere u>v. (Speed of sound in water is greater than speed of sound in air)Hence tair−tw=t⇒xv−xu=t⇒x(1v−1u)=t.Hence x=tuvu−v

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